Cambridge Additional Mathematics

Functions (Chapter 2) 53

EXERCISE 2F

1 Draw sign diagrams for these graphs:

abc

de f

gh i

jk l

Example 15 Self Tutor

Draw a sign diagram for:

a (x+ 3)(x¡1) b ¡4(x¡3)^2

a (x+ 3)(x¡1) has zeros¡ 3 and 1.

When x=2we have (5)(1)> 0 ,

so we put a+sign here.

As the factors are single, the signs

alternate.

b ¡4(x¡3)^2 has zero 3.

Whenx=4we have¡4(1)^2 < 0 ,

so we put a¡sign here.

As the factor is squared, the signs do

not change.

• 3 1

+ - +

x

3

--x

We substitute any number> 1.

-3 1

+

x

We substitute any number> 3.

3

• x

y

-2 O 2 x

y

O 1 x

y

x

x=-2¡¡ x=2¡¡

-1 1

O

y

x

x=-1¡¡

x=2

O

y

x

x=1

y=2

O 2

y

O 2 x

y

x

-1 3

O

y

O 2 x

y

x

-2

O

y

O x

y

-1 O 2 x

-3-3 4

x

y

O

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_02\053CamAdd_02.cdr Thursday, 3 April 2014 4:09:05 PM BRIAN